The double-slit experiment is the quintessential demonstration of wave-particle duality. In standard quantum mechanics, interference visibility v = (Imax − Imin)/(Imax + Imin) is unity for a perfectly coherent, isolated source. Any reduction is attributed to decoherence caused by environmental coupling. Here we propose an additional, intrinsic mechanism for visibility reduction that originates from the internal energy allocation of the quantum system itself, without requiring any loss of coherence. Energy-efficiency theory (EET) posits that any persistent localized system continuously allocates incoming energy between two competing channels: maintenance (E˙ main) that sustains the existing localized structure, and response (E˙ resp) that explores configuration space. Their ratio η = E˙ resp/E˙ main defines a dynamical regime. Standard quantum mechanics corresponds to the balanced equilibrium case η = 1. By externally driving the system, η can be tuned away from unity, leading to modified wavepacket spreading and, consequently, a reduced interference visibility even in the absence of decoherence. This paper presents a precise quantitative prediction for v(η), a feasible experimental realization using ultracold atoms in optical lattices, and a rigorous statistical protocol for falsification. The prediction is independent of any free parameters and can be tested with existing technology.
The double-slit experiment is the quintessential demonstration of wave-particle duality. In standard quantum mechanics, interference visibility v = (Imax − Imin)/(Imax + Imin) is unity for a perfectly coherent, isolated source. Any reduction is attributed to decoherence caused by environmental coupling. Here we propose an additional, intrinsic mechanism for visibility reduction that originates from the internal energy allocation of the quantum system itself, without requiring any loss of coherence. Energy-efficiency theory (EET) posits that any persistent localized system continuously allocates incoming energy between two competing channels: maintenance (E˙ main) that sustains the existing localized structure, and response (E˙ resp) that explores configuration space. Their ratio η = E˙ resp/E˙ main defines a dynamical regime. Standard quantum mechanics corresponds to the balanced equilibrium case η = 1. By externally driving the system, η can be tuned away from unity, leading to modified wavepacket spreading and, consequently, a reduced interference visibility even in the absence of decoherence. This paper presents a precise quantitative prediction for v(η), a feasible experimental realization using ultracold atoms in optical lattices, and a rigorous statistical protocol for falsification. The prediction is independent of any free parameters and can be tested with existing technology.
In standard quantum mechanics, the visibility of double-slit interference is determined solely by coherence and decoherence. Here we introduce a dimensionless parameter η = Ė_resp / Ė_main that quantifies the internal energy allocation between response (exploration) and maintenance (localization) of a quantum system. We show that even in the absence of decoherence, the visibility becomes v(η) = 2√η/(1+η) when the system is prepared in a non-equilibrium steady state with η ≠ 1. The derivation is based on an effective mass renormalization m* = m/η that preserves the standard Schrödinger form while scaling the dispersion rate. A concrete experimental realization using ultracold atoms in an optical lattice with amplitude modulation is proposed, together with a full statistical protocol to falsify the prediction. This provides a clean, experimentally accessible test of energy-efficiency theory (EET) against standard quantum mechanics.
The double‑slit experiment epitomizes the wave–particle duality of quantum mechanics. In standard treatments, the interference pattern follows from superposition, while measurement of “which path” destroys coherence. The precise mechanism that turns a coherent superposition into a localized detection event remains an open question. We propose an operator‑based model within the open‑quantum‑system framework that describes the entire process through seven effective Lindblad generators: fluctuating diffusion (initial wavepacket spreading), cyclic reset (quantum Zeno effect), spatial‑mode splitting (simultaneous excitation of both slits), free evolution (interference formation), liminal projection (threshold‑activated measurement), irreversible loss (detector inefficiency), and subspace mapping (projection onto a definite detection outcome). Unlike standard quantum mechanics, the model introduces a nonlinear decoherence rate that depends on the spatial spread of the wavefunction, capturing environment back‑action through a feedback‑controlled coupling. This dependence leads to a small but testable reduction of fringe visibility with increasing particle flux or wavepacket width, even in the absence of explicit which‑path measurement. The measurement activation is modeled as a smooth threshold function, giving a sharp transition in detection probability as the system reaches the screen. Analytical expressions for visibility and the critical Zeno frequency are derived, and numerical simulations are presented. The predictions are accessible with current experimental technology (weak measurements, controlled decoherence, cavity‑QED systems). The framework suggests that wave–particle duality can be understood as a dissipative phase transition, bridging foundational quantum theory with practical open‑system control.
The wave-particle duality of the electron is reinterpreted within Energy-Efficiency Theory (EET) as a continuous sliding of the energy ratio η = E˙ resp/E˙ main. In an atomic orbital, the electron is maintenance-dominated (η ≪ 1), exhibiting particle like localization. As a free wave packet, it is response-dominated (η ≫ 1), exhibiting wave-like delocalization. We derive the scaling relation ∆x ∝ η −1/2 from the exact solution of the modified Schr¨odinger equation and show that the Heisenberg uncertainty principle is preserved for all η. We propose an experimental protocol to continuously tune η using external microwave fields, thereby continuously controlling the electron’s interference visibility. Three falsifiable predictions are presented with explicit experimental designs, statistical criteria, and falsification conditions.
We present a unified energy-ontological interpretation of non-relativistic quantum mechanics within the framework of Energy-Efficiency Theory (EET). Starting from three physically grounded axioms, we define the constrained potential U(r,t) as the spatial density of localized bound-state energy, and derive the continuity equation for the normalized constrained potential ρ(r,t)=U(r,t)/E_c. We prove that ρ(r,t) satisfies the quantum probability continuity equation, establishing the exact correspondence ρ(r,t)=|ψ|^2. We introduce the dimensionless energy ratio η = Ė_resp / Ė_main, which quantifies the balance between energy allocated to spatial exploration (response) and constraint maintenance. From first principles, we derive a modified Schrödinger equation with a real effective potential that preserves probability conservation for all values of η. Using an exact analytical solution for Gaussian wave packets, we derive the scaling relations Δx ∝ η^{-1/2} and Δp ∝ η^{1/2}, which imply the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 independent of η. Wave-particle duality is interpreted as the continuous sliding of η between exploration-dominated (wave-like, η>1) and maintenance-dominated (particle-like, η<1) regimes. We extend the framework to quantum measurement, deriving the scaling of η from first-principles system-apparatus energy coupling, and unify projective measurements, weak measurements, the quantum eraser, and decoherence within a single framework. We present four experimentally falsifiable predictions with strict statistical criteria, along with a protocol for independent experimental control of η. This work provides a self-consistent energy-ontological foundation for non-relativistic quantum mechanics, unifying probability density, wave-particle duality, the uncertainty principle, and quantum measurement under a single energy allocation framework.
Abstract The relation between interference visibility and path distinguishability is a core pillar of quantum complementarity and decoherence theory. In standard quantum mechanics, all coherence decay in interferometric systems is attributed exclusively to path information leakage, which establishes a one-to-one relation between environmental distinguishability and fringe visibility. However, a fundamental question remains experimentally untested: whether discrete quantized energy exchange between light and matter can degrade quantum coherence independently of path distinguishability. In this work, we propose a high-precision cavity-QED experiment based on a Mach–Zehnder interferometer to decouple interaction modality from path information. A single trapped Rb atom inside an optical cavity is placed in one interferometer arm, enabling fully switchable light–matter interaction regimes: resonant discrete energy exchange and far-detuned continuous dispersive interaction. To eliminate systematic artifacts, we employ environmental state tomography to rigorously equalize the path distinguishability in both operational regimes. Furthermore, we systematically compensate all linear dynamical differences between resonant and dispersive cavity responses, including group delay, spectral distortion, and temporal mode mismatch. With all standard decoherence and dynamical contributions precisely calibrated, standard quantum mechanics predicts identical interference visibility for resonant and dispersive interactions. In contrast, a physically motivated alternative conjecture suggests that discrete energy exchange can induce intrinsic coherence suppression even at fixed path distinguishability. The two scenarios yield experimentally distinguishable visibility differences. Our scheme utilizes mature single-atom cavity quantum optics techniques without low-temperature superconducting devices, providing a robust and accessible platform to resolve this long-standing open question in quantum interferometry. The complete optical layout, timing sequence, tomography calibration, statistical criteria, and error suppression strategies are presented. This experiment offers a decisive experimental benchmark for the fundamental relationship between light–matter interaction type and quantum coherence.
This paper presents a conceptually economical reinterpretation of wave–particle duality, framing it as a consequence of dimensional projection rather than as a fundamental ontological dualism or an observer-induced collapse. Quantum systems are treated as evolving continuously within a space of effective informational degrees of freedom, while particle-like behavior emerges from restricted lower-dimensional access and irreversible recording. By reclassifying classic experiments—such as double-slit interference, delayed-choice setups, quantum erasers, and automated detection—under this framework, the work highlights that their empirically observed continuous behaviors are more naturally explained by projection and information restriction than by abrupt state reduction. Beyond reinterpretation, the paper introduces a falsifiable experimental criterion—the Dimensional Projection Test (DPT)—which distinguishes projection-based, no-collapse descriptions from genuine collapse models. The DPT predicts a smooth degradation of interference visibility under continuously tuned coupling, whereas any sharp transition would signal objective collapse dynamics. Positioned as complementary to existing collapse-model bounds rather than a competing formalism, the DPT provides an operational lens through which foundational ambiguities can be tested experimentally. Overall, the work clarifies long-standing conceptual confusion without modifying quantum mechanics, offering a disciplined, test-oriented contribution to quantum foundations. Reality does not change when we stop observing; only our access does.